It was a perfect lecture video for my Numerical Analysis course which made me understand everything about those norms and had me able to write down proofs so easily. Thanks for that
Dear Dr. Johnston, thank you so much for the great lectures! The explanation is so clear, and the intuition is well-illustrated. Thanks for your time and efforts to make such great teaching materials!!! Really appreciate it.
What is the difference between a spectral norm and an operator norm in terms of using the singular values of a matrix for their calculation? Could you please explain this using the example you gave at the end of the video?
Brilliant lecture, thanks a lot! I only a bit confused that the largest vector which represents the matrix transformation was not called eigenvector (so it's length would be the eigenvalue). Are they actually applicable terms in this context?
No, the largest vector is a singular vector, not an eigenvector, and the scaling factor is a singular value, not an eigenvalue. These concepts are the same for positive semidefinite matrices, but not in general.
Wonderful lecture !!!! I have no doubt that your lecture series on Advanced Linear Algebra is going to become a gold standard in the future.
Thank you for explaining concepts intuitively. I don't know why my professor cannot do that.
This is an excellent overview!
I have been listening to this series for nearly 2 months now, Time listening to this series is time well spent on learning linear algebra
It was a perfect lecture video for my Numerical Analysis course which made me understand everything about those norms and had me able to write down proofs so easily. Thanks for that
Wish I had found this channel earlier. Lectures are short and to the point.
loved it.
Thank you !
Dear Dr. Johnston, thank you so much for the great lectures! The explanation is so clear, and the intuition is well-illustrated. Thanks for your time and efforts to make such great teaching materials!!! Really appreciate it.
You have made so many concepts I was confused about click! Thank you 😊
KING. 👑
such a beautiful and smooth explanation !! Thank you sir
This series has helped me a lot
here i am rewatching a year later. thank you!
wondaful explanation ! Thanks :)
What is the difference between a spectral norm and an operator norm in terms of using the singular values of a matrix for their calculation? Could you please explain this using the example you gave at the end of the video?
The spectral norm and the operator norm are the same thing -- they're synonyms of each other.
@@NathanielMath Got it. Thank you so much Nathaniel! I just got back from class and was confused about these two haha...
Brilliant lecture, thanks a lot! I only a bit confused that the largest vector which represents the matrix transformation was not called eigenvector (so it's length would be the eigenvalue). Are they actually applicable terms in this context?
No, the largest vector is a singular vector, not an eigenvector, and the scaling factor is a singular value, not an eigenvalue. These concepts are the same for positive semidefinite matrices, but not in general.
@@NathanielMath Thank you for the clarification. That's really helpful!